Gravity SeriesLesson 10 of 11
How spatial geometry affects light
Clock-rate differences give a good description of a slow fall near Earth. Light passing the Sun lets us test the parts of spacetime geometry that this approximation leaves out.
The clock calculation in How clock rates connect with falling gave the familiar acceleration of a dropped ball. It worked because the ball moves slowly and Earth’s gravitational field is weak enough for a simplified calculation.
Spatial geometry also affects motion, but its additional contribution is small in that example. For light, we need to include it.
A ray passing the Sun
Imagine observing a distant star whose light passes close to the Sun on its way to Earth. Gravity bends the light, shifting the star’s apparent position in the sky.
A calculation that includes the gravitational difference in clock rates but treats space as flat predicts a bend of about 0.88 arcseconds for a ray grazing the Sun. Including the spatial geometry gives about 1.75 arcseconds.
An arcsecond is one three-thousand-six-hundredth of a degree. The angle is small, but the difference between those predictions can be measured.
Comparing the prediction with an observation
During a total solar eclipse, the Sun is hidden enough for nearby stars to be photographed. Comparing those photographs with the same stars seen away from the Sun reveals the shift in their apparent positions.
The 1919 eclipse expeditions used this method as an early test of general relativity. Those measurements had limited precision; later observations have tested the predicted bending much more accurately.
Why the result doubles here
In this calculation, the spatial contribution adds approximately as much bending as the clock-rate contribution. Together they give the full prediction.
The split is a useful way to follow the calculation, but depends on how we describe space and time. The total deflection is the measurable result. We cannot extend this particular factor of two into a rule that light always bends twice as much as matter.
Bringing space and time together
Einstein’s equations relate matter and energy to spacetime geometry. That geometry determines the free paths of objects and light. The clock-rate calculation captures much of what matters for a slow fall near Earth; the light-deflection calculation needs more of the description.
We have now used falling objects, clocks and light to explore the same spacetime description. The final lesson brings those observations together around one Earth, so we can see how standing, falling and orbiting fit into the same explanation.